Rupert Murdoch told the Leveson inquiry that News International wanted 'to create a lasting legacy' with an academy in Newham. Photograph: Graham Turner for the Guardian

News International offered £2m in sponsorship to create an academy school but the plans fell through because the Department for Education could not afford to pay for a new building, according to email exchanges (pdf) published by the Leveson inquiry.

In an email sent in January last year, a senior DfE civil servant acknowledged the Sun, Times and Sunday Times publisher's desire for a new building but regretted that there was no government funding available for it.

"In our discussions last year we explored the options and you set some parameters for what a News International Academy would be," the official wrote. "It could not be a replacement for a failing local school, as in the traditional model for sponsored academies. It would need to be a new school and it was important to News International that the new building made a significant statement about News International's commitment."

The official said there was no funding for a new building because of the "very tight" spending review.

The emails show that News International persisted with its attempt to establish a new state school. In an email sent in May last year, the company's head of corporate affairs, Daisy Dunlop, wrote: "I am aware that the deadline for free school applications is the 1st June and I wondered if you thought that was a route we should be taking."

In his reply, the civil servant said: "The overall capital provision open to government has not changed significantly since we last spoke. An application to run a free school in Newham is certainly an option for you to pursue but the availability of resources for new buildings is likely to be very limited."

Dunlop responded by asking when the next round of applications would be, and was referred to the civil servant in charge of the free schools programme. In the course of his introductory email, the DfE official noted that Dunlop met the director of the free schools programme "when we visited your offices".

Throughout this period there was regular contact between the News International proprietor, Rupert Murdoch, and Michael Gove, the education secretary. The pair had dinner five times, as well as a lunch and a breakfast, between May 2010 and June last year, according to the DfE (pdf).

Asked at the Leveson inquiry on Thursday whether Gove was close to him, Murdoch replied: "I wish he was."

In his evidence he described the standard of public education in Britain and the US as "an absolute disgrace". Referring to education reform in the US, he said: "It's very difficult – not for lack of money but lack of teacher co-operation."

Murdoch said in his witness statement that: "NI's objective was to create a lasting legacy in east London, through an academy school with a focus on media and technology."

Academies are state-funded schools that are often managed by sponsors from business, charities, universities or private schools. When the programme was first set up under Labour, sponsors had to pay a share of the capital costs, capped at £2m.

Under the coalition, sponsors have not been required to make a financial contribution. Sponsors appoint a headteacher and work with them to develop the school's ethos and curriculum.